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Online Mixed Ring Covering Problem with Two Nodes

Author

Listed:
  • Man Xiao

    (Yunnan University)

  • Weidong Li

    (Yunnan University)

  • Xiaofei Liu

    (Yunnan University)

Abstract

In this paper, we study the online mixed ring covering problem, where the ring contains two nodes and undirected and bidirected links. A sequence of flows arrives one by one, where each flow has a traffic demand for each pair of nodes in the ring. The objective is to maximize the minimum load of the ring link, where the load of a link is the total demand of the flows sent to that link. We consider the problem in three different scenarios: splittable, integer splittable and unsplittable. When the demands are splittable, we present an optimal online algorithm with a competitive ratio that is no more than $$\frac{4}{3}$$ 4 3 . When the demands are integer splittable, we present an optimal online algorithm with a competitive ratio that is no more than 2. When the demands are unsplittable, we prove that the lower bound for this case is $$\infty$$ ∞ , and few researchers have provided this result. Then, we consider a special case of the online mixed ring covering problem when the demands are unsplittable, which has a buffer size of K, where K is the number of flows temporarily stored in the buffer. We prove that the competitive ratio for any positive integer K is at least 2. For $$K=1$$ K = 1 , we present an online algorithm with a competitive ratio that is no more than 3. For $$K=2$$ K = 2 , we present an online algorithm with a competitive ratio that is no more than $$\frac{3+\sqrt{5}}{2}\approx 2.618$$ 3 + 5 2 ≈ 2.618 .

Suggested Citation

  • Man Xiao & Weidong Li & Xiaofei Liu, 2023. "Online Mixed Ring Covering Problem with Two Nodes," SN Operations Research Forum, Springer, vol. 4(1), pages 1-20, March.
    • Handle: RePEc:spr:snopef:v:4:y:2023:i:1:d:10.1007_s43069-022-00189-x
    DOI: 10.1007/s43069-022-00189-x
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    References listed on IDEAS

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    1. Young-Soo Myung & Hu-Gon Kim & Dong-Wan Tcha, 1997. "Optimal Load Balancing on Sonet Bidirectional Rings," Operations Research, INFORMS, vol. 45(1), pages 148-152, February.
    2. Qingqin Nong & Jinjiang Yuan & Yixun Lin, 2009. "The weighted link ring loading problem," Journal of Combinatorial Optimization, Springer, vol. 18(1), pages 38-50, July.
    3. Yingli Ran & Yishuo Shi & Changbing Tang & Zhao Zhang, 2020. "A primal-dual algorithm for the minimum partial set multi-cover problem," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 725-746, April.
    Full references (including those not matched with items on IDEAS)

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